In the bowl of a stand mixer or in a medium bowl with an electric mixer, beat the butter and sugar together on medium speed until fluffy, about 3 minutes. Add in the egg white, vanilla extract, and peppermint extract and beat until combined.

In a small bowl, whisk the flour, cocoa powder, and salt together.

With the mixer on low, mix the flour mixture into the butter mixture until a dough is formed. Shape the dough into a flattened disc, then wrap well and refrigerate until firm, about 2 hours.

When ready to bake, preheat the oven to 350°F (180°C) and line two baking sheets with parchment paper.

On a floured surface, roll the dough out to ⅛-inch-thick (3 mm) and with a 2-inch (5-cm) round cutter, cut out as many circles of dough as you can. You can gather and reroll any scraps. Place the cookies 1½ inches (3 cm) apart on the prepared baking sheets.

Bake for 15 to 18 minutes, until the cookies look dry and baked. Transfer to a wire rack to cool completely and set the parchment-lined baking sheets aside.

In a double boiler or in a microwave-safe bowl, combine the chocolate, peppermint extract, vanilla extract, and vegetable oil and heat gently, stirring frequently, until melted.

Using a fork, immerse each cookie in the chocolate, then lift out and return to the baking sheets to set completely before serving and storing. (you can also pop them into the fridge). Store in an airtight container at room temperature for up to 3 days.